I'd like my Screen to stay dark for SMS and incoming call notificationSupport

Hi just got my first smart phone. The new DX and I love it. It's fast and great. I'm a heavy user so I'd like to conserve as much battery as possible.Is it possible to have the screen not light up when I get an SMS or a call?I'd like my phone to just ring without lighting up because I get tons of SMS for my work.thank you for your help.